Doesn't anyone else find the solution a bit problematic: sure great concept but unless the guards have a black box tool which is secured and can churn out Y from X, they will have to know the function to prove that Y was congruent with an X...and if they know the function, so too would the enemy. On the other hand if they have a secure tool that does this fine, but this seems to simplify the problem considerably b/c the key is that the guard doesn't need to know anything at all: the tool does all the work.